irrelevantIdeal -- gives the irrelevant ideal of the coordinate ring of a product of projective spaces

Synopsis

Usage:

irrelevantIdeal R
Inputs:
- R, a ring, coordinate ring of a product of projective spaces
Outputs:
- an ideal, irrelevant ideal in R

Description

Given the coordinate ring of a product of projective spaces, this function produces the irrelevant ideal (in the sense of toric geometry) by listing the unique degrees of generators of R, creating an ideal from the generators of each degree, and intersecting them.

i1 : R = multigradedPolynomialRing {1,2}

o1 = R

o1 : PolynomialRing

i2 : irrelevantIdeal R

o2 = ideal (x   x   , x   x   , x   x   , x   x   , x   x   , x   x   )
             0,1 1,2   0,0 1,2   0,1 1,1   0,0 1,1   0,1 1,0   0,0 1,0

o2 : Ideal of R

i3 : R = multigradedPolynomialRing 3

o3 = R

o3 : PolynomialRing

i4 : irrelevantIdeal R

o4 = ideal (x   x   x   , x   x   x   , x   x   x   , x   x   x   ,
             0,1 1,1 2,1   0,0 1,1 2,1   0,1 1,0 2,1   0,0 1,0 2,1 
     ------------------------------------------------------------------------
     x   x   x   , x   x   x   , x   x   x   , x   x   x   )
      0,1 1,1 2,0   0,0 1,1 2,0   0,1 1,0 2,0   0,0 1,0 2,0

o4 : Ideal of R

Caveat

This function will not give the correct irrelevant ideal for the Cox ring of a toric variety that is not a product of projective spaces. Use the package NormalToricVarieties instead.

Ways to use irrelevantIdeal :

irrelevantIdeal(Ring)

For the programmer